Name: cable tension under uniform loading
Uploaded: 2025-05-22T09:06:04.000Z
Duration: 1 min 29 s
Channel: JoVE

Considere um cabo fixado em dois suportes sujeitos a carga uniforme. Determine a tensão máxima no cabo.
Para análise, considere a origem no centro do cabo devido à sua simetria.
Recupere a equação de forma do cabo para carga distribuída e substitua o valor de carga constante conhecido.
Em seguida, integre a equação e, aplicando as condições de contorno na origem, a constante C2 é determinada.
Tomando a primeira derivada da equação da forma do cabo, a inclinação pode ser determinada. Aplicando as condições de contorno para a inclinação na origem, C1 é obtido.
Substituindo as constantes de integração e as coordenadas de posição do apoio e reorganizando a equação, obtém-se a força de tração horizontal.
Recupere a equação de inclinação e substitua o valor da coordenada x no suporte onde o ângulo é máximo.
A tensão de Cabel muda com o ângulo, que é o suporte máximo próximo.
Aplicando a relação trigonométrica e reorganizando os termos, obtém-se a equação de tensão máxima.
Finalmente, substituindo a equação de tensão horizontal e os valores conhecidos, obtém-se a tensão máxima no cabo.

<ol>
	<li>Hibbeler, R.C. (2016). Engenharia Mecânica \u2012 Estática e Dinâmica. Hoboken, Nova Jersey: Pearson Prentice Hall. pág. 384-385, 393.</li>
</ol>

cabo: solução de problemas

Ao lidar com um cabo fixo em dois suportes e submetido a uma carga uniforme, é crucial determinar a tensão máxima no cabo. Esse processo pode ser dividido em várias etapas-chave, como descrito abaixo:

<img alt="Figure 1" src="/files/ftp_upload/14310/14310_Figure_1v3.svg" style="text-align: center; height: 300px;" />

Analise o problema: Comece entendendo o cenário apresentado e as condições do cabo. Identifique os suportes, o tipo de carga e qualquer outra informação relevante.

Determine a equação da forma do cabo: Use os princípios de equilíbrio e as propriedades do cabo para estabelecer a equação da forma que descreve a curva do cabo. Essa equação relaciona a forma do cabo com a carga aplicada.

<img alt="Equation 1" src="/files/ftp_upload/14310/14310_Equation_1v2.svg" style="text-align: center; height: 35px;" />

Integre a equação: Integre a equação da forma para obter uma função que representa a forma do cabo. Esse processo de integração permite determinar as constantes na equação. Ao aplicar as condições de contorno na origem, é possível determinar o valor de uma das constantes de integração.

<img alt="Equation 2" src="/files/ftp_upload/14310/14310_Equation_2v2.svg" style="text-align: center; height: 35px;" />

Encontre a inclinação: Faça a primeira derivada da equação da forma do cabo para determinar a inclinação do cabo em qualquer ponto. Aplique as condições de contorno para a inclinação na origem para obter o valor de outra constante de integração.

Calcule a força de tração horizontal: Substitua as constantes de integração e as coordenadas de posição do suporte na equação da forma. Rearranje os termos para encontrar a força de tração horizontal atuando no cabo.

<img alt="Equation 3" src="/files/ftp_upload/14310/14310_Equation_3v2.svg" style="text-align: center; height: 35px;" />

Determine o ângulo: Use a equação da inclinação para calcular o ângulo do cabo em vários pontos. Encontre a posição ao longo do cabo onde o ângulo é máximo, geralmente próximo aos suportes. Utilize relações trigonométricas para expressar a tensão máxima em termos da força de tração horizontal e do ângulo do cabo.

<img alt="Equation 4" src="/files/ftp_upload/14310/14310_Equation_4v2.svg" style="text-align: center; height: 35px;" />

Encontre a tensão máxima: Substitua a equação da tensão horizontal e os valores conhecidos na equação da tensão máxima. Isso permitirá calcular a tensão máxima no cabo.

<img alt="Equation 5" src="/files/ftp_upload/14310/14310_Equation_5v2.svg" style="text-align: center; height: 40px;" />

Cabo: Solução de problemas

Ao lidar com um cabo fixado a dois suportes e submetido a um carregamento uniforme, é crucial determinar a tensão máxima no cabo. ...

Education

JoVE Core

Mechanical Engineering

Engenharia Mecânica

Unit 1

Unidade 1

Internal Forces

Forças Internas

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

Cable: Problem Solving

cable tension under uniform loading

Cable tension under uniform loading is found by analyzing a cable fixed between two supports. The problem starts with the support conditions and the load on the cable. From there, the cable’s shape must be described with an equation that matches the curve formed by the load.

The next step is to integrate the shape equation to get the cable’s shape function. This makes it possible to solve for constants in the equation. The boundary condition at the origin gives one constant. The slope, which is the first derivative of the shape equation, gives the cable’s tilt at any point. A second boundary condition at the origin is used to find another constant.

After the constants are set, the horizontal tensile force can be calculated from the support coordinates and the shape equation. The slope equation is then used to find the cable angle at different points. The angle is usually largest near the supports, so that location is used to determine the maximum tension.

Trigonometric relationships connect the maximum tension to the horizontal tensile force and the cable angle. Once the horizontal tension equation and the given values are substituted into the tension formula, the maximum tension in the cable can be found.

Cable Tension Under Uniform Loading

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cable: problem solving

Cable tension under uniform loading is found by analyzing a cable fixed between two supports. The problem starts with the support conditions and the load on the cable. From there, the cable’s shape must be described with an equation that matches the curve formed by the load. The next step is to integrate the shape equation to get the cable’s shape function. This makes it possible to solve for constants in the equation. The boundary condition at the origin gives one constant. The slope, which...

key terms and concepts

Follow the steps to find maximum cable tension under uniform loading using the cable shape equation, slope, boundary conditions, and trigonometry.

Cable Tension Under Uniform Loading | JoVE K12

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Cable Tension Under Uniform Loading

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